Attocube - Test Bench

The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\).

load('./mat/long_test2.mat', 'x', 't')
Ts = 0.1; % [s]

Let’s fit the data with a step response to a first order low pass filter (Figure 2).

f = @(b,x) b(1)*(1 - exp(-x/b(2)));

y_cur = x(t < 17*60*60);
t_cur = t(t < 17*60*60);

nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
B0 = [400e-9, 2*60*60];                        % Choose Appropriate Initial Estimates
[B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’

The corresponding time constant is (in [h]):

2.0576

We can see in Figure 1 that there is a transient period where the measured displacement experiences some drifts. This is probably due to thermal effects. We only select the data between t1 and t2. The obtained displacement is shown in Figure 3.

t1 = 11; t2 = 17; % [h]

x = x(t > t1*60*60 & t < t2*60*60);
x = x - mean(x);
t = t(t > t1*60*60 & t < t2*60*60);
t = t - t(1);

The Power Spectral Density of the measured displacement is computed

win = hann(ceil(length(x)/20));
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);

An second measurement is done in order to estimate the high frequency noise of the interferometer. The measurement is done with a sampling time of \(T_s = 0.1\,ms\) and a duration of ~100s.

load('./mat/test.mat', 'x', 't')
Ts = 1e-4; % [s]

The time domain measurement is shown in Figure 4.

The Power Spectral Density of the measured displacement is computed

win = hann(ceil(length(x)/20));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);

The computed ASD of the two measurements are combined in Figure 5.